Subgroups — C₉×#5730 #13153311

Order 1728.

752 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#946	C₂	1	4	yes	maximal, complemented
3	C₉×#897	C₂	1	2	yes	maximal, complemented
4	C₉×#893	C₂	1	2	yes	maximal
5	D₃×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₉×#890	C₂	1	2	yes	maximal, complemented
7	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic
8	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5730	C₃	1	1	yes	maximal, characteristic
10	C₉×#554	—	3	1	no	maximal
11	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
12	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
14	C₂×C₄×D₃×C₉	C₂²	1	4	yes	—
15	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
16	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
17	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
19	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
20	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
21	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
22	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₉×C₄⋊Dic₃	C₂²	1	4	yes	—
24	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
25	C₉×Dic₃⋊C₄	C₂²	1	4	yes	—
26	C₄×C₉×Dic₃	C₂²	1	2	yes	—
27	C₃²×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
28	C₃×#946	C₂×C₃	1	4	yes	—
29	C₃×#897	C₂×C₃	1	2	yes	—
30	C₃×#893	C₂×C₃	1	2	yes	—
31	C₃×D₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
32	C₃×#890	C₂×C₃	1	2	yes	—
33	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
34	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
35	C₉×C₄⋊Q₈	—	2	1	no	—
36	C₉×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
37	C₉×#125	—	3	2	no	—
38	C₉×C₂²⋊Q₈	—	3	4	no	—
39	C₉×C₂²⋊Q₈	—	3	2	no	—
40	C₄×Q₈×C₉	—	3	1	no	—
41	C₄×D₄×C₉	—	3	2	no	—
42	C₄×D₄×C₉	—	3	1	no	—
43	C₂×C₉×C₄⋊C₄	—	3	2	no	—
44	C₂²×D₃×C₉	C₂³	1	2	yes	—
45	C₃×Q₈×C₉	—	4	2	no	—
46	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×C₉×Dic₃	C₂³	1	2	yes	—
51	C₂×C₉×Dic₃	C₂³	1	2	yes	—
52	C₂×C₉×Dic₃	C₂³	1	2	yes	—
53	C₉×D₁₂	Q₈	1	4	yes	complemented
54	C₄×D₃×C₉	—	2	4	no	—
55	C₄×D₃×C₉	—	4	4	no	—
56	C₉×Dic₆	—	2	2	no	—
57	C₃×#554	—	3	1	no	—
58	#5730	C₉	1	1	yes	characteristic, direct product factor
59	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
60	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
61	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
62	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
63	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
64	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
65	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
66	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
67	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
68	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
69	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
70	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
71	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
72	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
73	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
74	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
75	C₂×Q₈×C₉	—	2	2	no	—
76	C₂×Q₈×C₉	—	3	1	no	—
77	C₂×Q₈×C₉	C₂×D₃	1	2	yes	—
78	C₂×D₄×C₉	—	3	1	no	—
79	C₂²×C₄×C₉	—	3	2	no	—
80	C₂²×C₄×C₉	—	3	4	no	—
81	C₉×C₄⋊C₄	—	2	2	no	—
82	C₉×C₄⋊C₄	—	2	2	no	—
83	C₉×C₄⋊C₄	—	3	1	no	—
84	C₉×C₄⋊C₄	—	3	4	no	—
85	C₉×C₄⋊C₄	—	3	1	no	—
86	C₉×C₄⋊C₄	—	3	2	no	—
87	C₉×C₄⋊C₄	—	3	4	no	—
88	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
89	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
90	C₉×C₂²⋊C₄	—	3	4	no	—
91	C₉×C₂²⋊C₄	—	3	2	no	—
92	C₄²×C₉	—	2	1	no	—
93	C₄²×C₉	—	3	2	no	—
94	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
95	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
96	C₂×D₃×C₉	—	2	2	no	—
97	C₂×D₃×C₉	—	2	2	no	—
98	C₂×D₃×C₉	C₂×Q₈	1	4	yes	—
99	C₃×C₄×C₉	—	2	1	no	—
100	C₃×C₄×C₉	—	2	4	no	—
101	C₃×C₄×C₉	C₂×Q₈	1	2	yes	—
102	C₃×C₄×C₉	#41	1	2	yes	—
103	C₉×Dic₃	—	2	2	no	—
104	C₉×Dic₃	—	2	2	no	—
105	C₉×Dic₃	—	2	2	no	—
106	C₃×C₄⋊Q₈	—	2	1	no	—
107	C₃×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
108	C₃×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic
109	C₃×#125	—	3	2	no	—
110	C₃×C₂²⋊Q₈	—	3	4	no	—
111	C₃×C₂²⋊Q₈	—	3	2	no	—
112	C₃×C₄×Q₈	—	3	1	no	—
113	C₃×C₄×D₄	—	3	2	no	—
114	C₃×C₄×D₄	—	3	1	no	—
115	C₂×C₃×C₄⋊C₄	—	3	2	no	—
116	#946	C₂×C₉	1	4	yes	complemented
117	#897	C₂×C₉	1	2	yes	complemented
118	#893	C₂×C₉	1	2	yes	—
119	D₃×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
120	#890	C₂×C₉	1	2	yes	complemented
121	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic
122	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
123	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
124	C₃²×Q₈	—	4	2	no	—
125	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
127	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
129	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
130	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
131	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
132	C₃×D₁₂	C₃×Q₈	1	4	yes	—
133	C₃×C₄×D₃	—	2	4	no	—
134	C₃×C₄×D₃	—	4	4	no	—
135	C₃×Dic₆	—	2	2	no	—
136	C₂³×C₉	—	3	2	no	—
137	Q₈×C₉	—	4	2	no	—
138	Q₈×C₉	—	4	4	no	—
139	Q₈×C₉	—	6	2	no	—
140	D₄×C₉	—	3	4	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	4	no	—
145	C₂×C₄×C₉	—	3	2	no	—
146	C₂×C₄×C₉	—	3	2	no	—
147	C₂×C₄×C₉	—	3	2	no	—
148	C₂×C₄×C₉	—	6	4	no	—
149	C₂×C₄×C₉	—	12	4	no	—
150	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
151	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
152	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
153	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
154	#554	—	3	1	no	Sylow
155	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
157	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
158	D₃×C₉	—	2	4	no	—
159	C₂×C₃×Q₈	—	2	2	no	—
160	C₂×C₃×Q₈	—	3	1	no	—
161	C₂×C₃×Q₈	C₂²×C₉	1	2	yes	—
162	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
163	C₂×C₃×D₄	—	3	1	no	—
164	C₂²×C₃×C₄	—	3	2	no	—
165	C₂²×C₃×C₄	—	3	4	no	—
166	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
167	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
168	C₂×C₄×D₃	C₂²×C₉	1	4	yes	—
169	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	3	4	no	—
173	C₃×C₄⋊C₄	—	3	2	no	—
174	C₃×C₄⋊C₄	—	3	1	no	—
175	C₃×C₄⋊C₄	—	3	1	no	—
176	C₃×C₄⋊C₄	—	3	4	no	—
177	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
178	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
179	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
180	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
181	C₃×C₂²⋊C₄	—	3	4	no	—
182	C₃×C₂²⋊C₄	—	3	2	no	—
183	C₃×C₄²	—	2	1	no	—
184	C₃×C₄²	—	3	2	no	—
185	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
186	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
187	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
188	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
189	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
190	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
191	C₄⋊Dic₃	C₂²×C₉	1	4	yes	—
192	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
193	Dic₃⋊C₄	C₂²×C₉	1	4	yes	—
194	C₄×Dic₃	C₂²×C₉	1	2	yes	—
195	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
196	C₂×C₃×D₃	—	2	2	no	—
197	C₂×C₃×D₃	—	2	2	no	—
198	C₂×C₃×D₃	C₂×C₃×Q₈	1	4	yes	—
199	C₃²×C₄	—	2	1	no	—
200	C₃²×C₄	—	2	4	no	—
201	C₃²×C₄	C₂×C₃×Q₈	1	2	yes	—
202	C₃²×C₄	C₃×#41	1	2	yes	—
203	C₃×Dic₃	—	2	2	no	—
204	C₃×Dic₃	—	2	2	no	—
205	C₃×Dic₃	—	2	2	no	—
206	C₂²×C₉	—	2	1	no	—
207	C₂²×C₉	—	3	4	no	—
208	C₂²×C₉	—	6	2	no	—
209	C₂²×C₉	—	6	2	no	—
210	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
211	C₄×C₉	—	2	2	no	—
212	C₄×C₉	—	2	4	no	—
213	C₄×C₉	—	2	1	no	—
214	C₄×C₉	—	2	2	no	—
215	C₄×C₉	—	2	2	no	—
216	C₄×C₉	—	4	4	no	—
217	C₄×C₉	—	6	2	no	—
218	C₄×C₉	—	6	2	no	—
219	C₄×C₉	—	6	2	no	—
220	C₄×C₉	D₃×Q₈	1	2	yes	—
221	C₄×C₉	#239	1	2	yes	—
222	C₄⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
223	#125	—	3	2	no	—
224	C₂²⋊Q₈	—	3	4	no	—
225	C₂²⋊Q₈	—	3	2	no	—
226	C₄×Q₈	—	3	1	no	—
227	C₄×D₄	—	3	2	no	—
228	C₄×D₄	—	3	1	no	—
229	C₂×C₄⋊C₄	—	3	2	no	—
230	C₃×C₉	#554	1	1	yes	characteristic, complemented, Sylow
231	C₂³×C₃	—	3	2	no	—
232	C₂²×D₃	C₂³×C₉	1	2	yes	—
233	C₃×Q₈	—	4	2	no	—
234	C₃×Q₈	—	4	2	no	—
235	C₃×Q₈	—	4	4	no	—
236	C₃×Q₈	—	6	2	no	—
237	C₃×D₄	—	3	4	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	3	2	no	—
243	C₂×C₃×C₄	—	3	2	no	—
244	C₂×C₃×C₄	—	3	2	no	—
245	C₂×C₃×C₄	—	6	4	no	—
246	C₂×C₃×C₄	—	12	4	no	—
247	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
249	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
253	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
255	C₂×Dic₃	C₂³×C₉	1	2	yes	—
256	C₂×Dic₃	C₂³×C₉	1	2	yes	—
257	C₂×Dic₃	C₂³×C₉	1	2	yes	—
258	D₁₂	Q₈×C₉	1	4	yes	complemented
259	C₄×D₃	—	2	4	no	—
260	C₄×D₃	—	4	4	no	—
261	Dic₆	—	2	2	no	—
262	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
263	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
264	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
265	C₃×D₃	—	2	4	no	—
266	C₂×C₉	—	2	1	no	—
267	C₂×C₉	—	2	1	no	—
268	C₂×C₉	—	2	1	no	—
269	C₂×C₉	—	6	4	no	—
270	C₂×C₉	#1004	1	1	yes	characteristic
271	C₂×C₉	C₂×D₃×Q₈	1	1	yes	characteristic
272	C₂×C₉	C₂×#239	1	1	yes	characteristic
273	C₂×Q₈	—	3	1	no	—
274	C₂×Q₈	C₂×D₃×C₉	1	2	yes	—
275	C₂×D₄	—	3	1	no	—
276	C₂²×C₄	—	3	2	no	—
277	C₂²×C₄	—	3	4	no	—
278	C₄⋊C₄	—	3	1	no	—
279	C₄⋊C₄	—	3	4	no	—
280	C₄⋊C₄	—	3	1	no	—
281	C₄⋊C₄	—	3	2	no	—
282	C₄⋊C₄	—	3	4	no	—
283	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
284	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
285	C₂²⋊C₄	—	3	4	no	—
286	C₂²⋊C₄	—	3	2	no	—
287	C₄²	—	3	2	no	—
288	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	3	4	no	—
291	C₂²×C₃	—	6	2	no	—
292	C₂²×C₃	—	6	2	no	—
293	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
294	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
295	C₂×D₃	—	2	2	no	—
296	C₂×D₃	—	2	2	no	—
297	C₂×D₃	C₂×Q₈×C₉	1	4	yes	—
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	2	4	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	2	4	no	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	4	4	no	—
306	C₃×C₄	—	6	2	no	—
307	C₃×C₄	—	6	2	no	—
308	C₃×C₄	—	6	2	no	—
309	C₃×C₄	C₂×Q₈×C₉	1	2	yes	—
310	C₃×C₄	C₉×#41	1	2	yes	—
311	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
312	C₃×C₄	C₃×#239	1	2	yes	—
313	Dic₃	—	2	2	no	—
314	Dic₃	—	2	2	no	—
315	Dic₃	—	2	2	no	—
316	C₃²	C₃×#554	1	1	yes	characteristic
317	C₉	—	2	1	no	—
318	C₉	#5730	1	1	yes	characteristic, direct product factor
319	C₂³	—	3	2	no	—
320	Q₈	—	4	2	no	—
321	Q₈	—	6	2	no	—
322	D₄	—	3	4	no	—
323	C₂×C₄	—	3	2	no	—
324	C₂×C₄	—	3	2	no	—
325	C₂×C₄	—	3	2	no	—
326	C₂×C₄	—	6	4	no	—
327	C₂×C₄	—	12	4	no	—
328	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
329	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
330	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
332	C₂×C₃	—	2	1	no	—
333	C₂×C₃	—	2	1	no	—
334	C₂×C₃	—	2	1	no	—
335	C₂×C₃	—	6	4	no	—
336	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
337	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
338	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₃	C₃×#1004	1	1	yes	characteristic
340	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
341	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
342	D₃	—	2	4	no	—
343	C₂²	—	3	4	no	—
344	C₂²	—	6	2	no	—
345	C₂²	—	6	2	no	—
346	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	2	1	no	—
349	C₄	—	6	2	no	—
350	C₄	—	6	2	no	—
351	C₄	—	6	2	no	—
352	C₄	D₃×Q₈×C₉	1	2	yes	—
353	C₄	C₉×#239	1	2	yes	—
354	C₃	—	2	1	no	—
355	C₃	C₉×#554	1	1	yes	characteristic, complemented
356	C₃	C₃×#5730	1	1	yes	characteristic
357	C₂	—	6	4	no	—
358	C₂	C₉×#1004	1	1	yes	characteristic
359	C₂	C₂×D₃×Q₈×C₉	1	1	yes	characteristic
360	C₂	C₂×C₉×#239	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×C₄⋊Q₈	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×D₁₂	C₂²×C₃
hypercenter	C₉×C₄⋊Q₈	D₃
hypocenter	C₃	C₉×#554
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×C₄⋊Q₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₉×C₄⋊Q₈	C₂	semidirect
2. C₉×#946	C₂	semidirect
3. C₉×#897	C₂	semidirect
5. D₃×C₉×C₄⋊C₄	C₂	semidirect
6. C₉×#890	C₂	semidirect
8. C₄×C₉×Dic₆	C₂	semidirect
36. C₉×C₄⋊Q₈	D₃	semidirect
53. C₉×D₁₂	Q₈	semidirect
58. #5730	C₉	direct (N × H)
107. C₃×C₄⋊Q₈	C₂×C₉	semidirect
116. #946	C₂×C₉	semidirect
117. #897	C₂×C₉	semidirect
119. D₃×C₄⋊C₄	C₂×C₉	semidirect
120. #890	C₂×C₉	semidirect
122. C₄×Dic₆	C₂×C₉	semidirect
222. C₄⋊Q₈	D₃×C₉	semidirect
230. C₃×C₉	#554	semidirect
258. D₁₂	Q₈×C₉	semidirect
318. C₉	#5730	direct (N × H)
355. C₃	C₉×#554	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₉×C₄⋊Q₈	2
C₉×#946	2
C₉×#897	2
C₉×#893	2
D₃×C₉×C₄⋊C₄	2
C₉×#890	2
C₄×C₉×D₁₂	2
C₄×C₉×Dic₆	2
C₃×#5730	3
C₉×#554	3

Subgroups — C9×#5730 #13153311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5730 #13153311